This thesis presents two measurements of the properties of a two-dimensional Fermi gas. The first series of measurements examine the role of interactions in defining the dimensionality of the system. From this, the parameter space where two-dimensional kinematics can be observed is established. Using this result, the thermodynamic properties and equations of state of an attractive Fermi gas in the normal phase are determined through the measurement of the density distribution of the trapped gas.
This thesis presents two measurements of the properties of a two-dimensional Fermi gas. The first series of measurements examine the role of interactions in defining the dimensionality of the system. From this, the parameter space where two-dimensional kinematics can be observed is established. Using this result, the thermodynamic properties and equations of state of an attractive Fermi gas in the normal phase are determined through the measurement of the density distribution of the trapped gas.
Thermodynamic properties of matter are conveniently expressed as functional relations between variables known as equations of state. Here we experimentally determine the compressibility, density, and pressure equations of state for an attractive 2D Fermi gas in the normal phase as a function of temperature and interaction strength. In 2D, interacting gases exhibit qualitatively different features to those found in 3D. This is evident in the normalized density equation of state, which peaks at intermediate densities corresponding to the crossover from classical to quantum behavior.
The physical properties of a homogeneous system at the thermodynamic equilibrium are strongly constrained by its dimensionality. In this respect, the two dimensional Bose gas constitutes a particularly interesting system: while it is impossible to observe a long range order at non-zero temperatures, there exists nevertheless a phase transition to a superfluid state at low temperatures. Furthermore, owing to the reduced dimensionality, the equation of state of the weakly interacting two-dimensional Bose gas is scale invariant. In this thesis, we present an experimental study of the two-dimensional Bose gas. We measure its equation of state with two different methods, and find a good agreement with analytic and numerical predictions. These results confirm as well the scale invariance of the system. Furthermore, one of the methods allows for a determination of the equation of state with a single adjustable parameter. We then characterize the superfluid response of the system., by showing evidence for a dissipationless response of the system to a moving perturbation. Finally, we analyze the fluctuations dynamics of the 2D Bose gas, which confirms both the suppression of density fluctuations in the superfluid phase, and the dominating contribution of phonons to the phase fluctuations.
Fermionic matter is ubiquitous in nature, from the electrons in metals and semiconductors or the neutrons in the inner crust of neutron stars, to gases of fermionic atoms, like 40K or 6Li that can be created and studied under laboratory conditions. It is especially interesting to study these systems at very low temperatures, where we enter the world of quantum mechanical phenomena. Due to the Fermi-Dirac statistics, a dilute system of spin-polarised fermions exhibits no interactions and can be viewed as an ideal Fermi gas. However, interactions play a crucial role for fermions of several spin species. This thesis addresses several questions concerning interacting Fermi gases, in particular the transition between the normal and the superfluid phase and dynamical properties at higher temperatures. First we will look at the unitary Fermi gas: a two-component system of fermions interacting with divergent scattering length. This system is particularly interesting as it exhibits universal behaviour. Due to the strong interactions perturbation theory is inapplicable and no exact theoretical description is available. I will describe the Determinant Diagrammatic Monte Carlo algorithm with which the unitary Fermi gas can be studied from first principles. This algorithm fails in the presence of a spin imbalance (unequal number of particles in the two components) due to a sign problem. I will show how to apply reweighting techniques to generalise the algorithm to the imbalanced case, and present results for the critical temperature and other thermodynamic observables at the critical point, namely the chemical potential, the energy per particle and the contact density. These are the first numerical results for the imbalanced unitary Fermi gas at finite temperature. I will also show how temperatures beyond the critical point can be accessed and present results for the equation of state and the temperature dependence of the contact density. At sufficiently high temperatures a semiclassical description captures all relevant physical features of the system. The dynamics of an interacting Fermi gas can then be studied via a numerical simulation of the Boltzmann equation. I will describe such a numerical setup and apply it to study the collision of two spin-polarised fermionic clouds. When the two components are separated in an elongated harmonic trap and then released, they collide and for sufficiently strong interactions can bounce off each other several times. I will discuss the different types of the qualitative behaviour, show how they can be interpreted in terms of the equilibrium properties of the system, and explain how they relate to the coupling between different excitation modes. I will also demonstrate how transport coefficients, for instance the spin drag, can be extracted from the numerical data.
We present results on the effect of short-range, attractive interactions on the properties of balanced tw-dimensional Fermi gases in the nonsuperfluid (normal) phase. Our approach combines the renormalization group (RG) with perturbation theory, yielding observables such as the equation of state and compressibility. We find good agreement with recent experiments that measured the equation of state in trapped gases in the balanced regime, showing that these results are consistent with logarithmic corrections in the equation of state.
Thermodynamic properties of matter generally depend on the details of interactions between its constituent parts. However, in a unitary Fermi gas where the scattering length diverges, thermodynamics is determined through universal functions that depend only on the particle density and temperature. By using only the general form of the equation of state and the equation of force balance, we measured the local internal energy of the trapped gas as a function of these parameters. Other universal functions, such as those corresponding to the Helmholtz free energy, chemical potential, and entropy, were calculated through general thermodynamic relations. The critical parameters were also determined at the superfluid transition temperature. These results apply to all strongly interacting fermionic systems, including neutron stars and nuclear matter.
Thermodynamic properties of matter generally depend on the details of interactions between its constituent parts. However, in a unitary Fermi gas where the scattering length diverges, thermodynamics is determined through universal functions that depend only on the particle density and temperature. By using only the general form of the equation of state and the equation of force balance, we measured the local internal energy of the trapped gas as a function of these parameters. Other universal functions, such as those corresponding to the Helmholtz free energy, chemical potential, and entropy, were calculated through general thermodynamic relations. The critical parameters were also determined at the superfluid transition temperature. These results apply to all strongly interacting fermionic systems, including neutron stars and nuclear matter.